A338400 - OEIS

%I #9 Jun 11 2022 01:19:51

%S 1,0,1,-2,2,-19,39,-257,1113,-6829,42399,-299550,2281531,-18901042,

%T 168402645,-1608304966,16381456532,-177291076953,2031597803009,

%U -24573784682206,312883002507064,-4182938253898882,58584703430964506,-857812167322107132,13106404407407087063

%N Inverse boustrophedon transform of the partition numbers.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BoustrophedonTransform.html">Boustrophedon Transform</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>

%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000111(n-k) * A000041(k).

%o (Python)

%o import sympy

%o def A338400(n):

%o   T=[]

%o   for k in range(n+1):

%o     T.append(sympy.npartitions(k))

%o     T.reverse()

%o     for i in range(k):

%o       T[i+1]=T[i]-T[i+1]

%o   return T[-1]

%o (Python)

%o from itertools import islice, count, accumulate

%o from operator import sub

%o from sympy import npartitions

%o def A338400_gen(): # generator of terms

%o     blist = tuple()

%o     for i in count(0):

%o         yield (blist := tuple(accumulate(reversed(blist),func=sub,initial=npartitions(i))))[-1]

%o A338400_list = list(islice(A338400_gen(),20)) # _Chai Wah Wu_, Jun 10 2022

%Y Cf. A000041, A000111, A000751.

%K sign

%O 0,4

%A _Pontus von Brömssen_, Oct 24 2020